SOLUTION: Write a logarithmic equation Use f(x) = log5(x) as the parent function. Ordered pair (-3,-2) y =

Question 1153723: Write a logarithmic equation
Use
f(x) = log5(x)
as the parent function. Ordered pair (-3,-2)
y =

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

We can have function(s) of the form

Given that the function is to have an integer value at x=-3, we want -3+b to be a power of 5.

(a) first example
5^0 = 1; -3+b = 1 --> b = 4

We want the function value at -3 to be -2, so we need to subtract 2. Our first function that satisfies the requirements is

A graph (window -10 to 10; -5 to 2):

(b) second example
5^1 = 5; -3+b = 5 --> b = 8

We want the function value at -3 to be -2, so we need to subtract 3. Our second function that satisfies the requirements is

A graph (window -10 to 10; -5 to 2), showing both graphs passing through (-3,-2):

We can also have functions of the form

Again using b=8,

We want the function value to be -2 at x=-3; so we can multiply this function by -2. Our third function that satisfies the requirements is

A graph again, showing the graphs of all three functions passing through (-3,-2):

You should be able to see that we can get as many functions as we want that satisfy the requirement.

Here is one more that gives the value -2 at x=-3:

One more graph, showing all four functions passing through (-3,-2):

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